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Koheles Rabba 7:2 says on the Pasuk "והחי יתן אל לבו" that Chazal say "Why do we knock on the heart? To say that everything originates from there." Therefore when a person has remorse on his sins, he knocks on the heart, to show that this is the source of the sin.

Rabbi Chaim, the brother of the Maharal M'Prag says that we knock with the hand since the Posuk in Iyov 37:7 says "וביד כל אדם יחתום" that the hands are witnesses on all that a person does and that is why in Devarim 17:7 it says "יד העדים תהיה בו בראשונה".

As an aside: The Minhag Chabad is only to knock on days that we recite Tachanun and never during Maariv.